On the reconstruction of graphs of connectivity $2$ having a $2$-vertex set dividing this graph into at least $3$ parts

Recall that the deck of a graph $G$ is the collection of subgraphs $G-v$ for all vertices $v$ of the graph $G$. Let $G$ be a of a $2$-connected graph having a $2$-vertex set dividing this graph into at least $3$ parts. We prove that $G$ is reconstructible by its deck. The proof contains an algorithm of the reconstruction.